RATIO AND PROPORTION

Ratio and Proportion is a core foundational chapter in CSAT. Though it appears simple, this topic tests an aspirant’s ability to compare quantities logically and apply proportional reasoning in real-life situations. Many CSAT questions from Mixture, Partnership, Average, Time & Work, and Data Interpretation are directly or indirectly based on ratio and proportion.

In OPSC Prelims, questions from this topic are generally:
• Conceptual and logic-based
• Calculation-light but reasoning-heavy
• Designed to test clarity rather than memorisation

MEANING OF RATIO

• A ratio is a comparison between two quantities of the same kind
• It tells how many times one quantity is greater or smaller than the other

Representation
• Written using colon (:)
• Example: Ratio of 10 and 20 = 10:20 = 1:2

Important Point
• Quantities compared must be of the same unit
• Units should be converted before forming ratio

SIMPLIFICATION OF RATIO

Steps
1. Write the ratio
2. Divide both terms by their HCF
3. Express the simplest form

Example
• 18:24
• HCF = 6
• Simplified ratio = 3:4

TYPES OF RATIOS

4.1 Simple Ratio
• Direct comparison between two quantities
• Example: Age of A and B = 20:30 = 2:3

4.2 Compound Ratio
• Ratio obtained by multiplying two or more ratios
• Example:
  (2:3) and (4:5)
  Compound ratio = (2×4):(3×5) = 8:15

 PROPORTION

Meaning
• Proportion is an equality of two ratios

Representation
• a:b = c:d

Condition
• a × d = b × c

Example
• 2:3 = 4:6
• 2 × 6 = 3 × 4

DIRECT PROPORTION

Definition
• Two quantities are directly proportional if increase in one leads to increase in the other in same ratio

Examples
• Cost and quantity
• Distance and time (at constant speed)
• Wages and work done

Mathematical Form
• x ∝ y
• x/y = constant

INVERSE PROPORTION

Definition
• Two quantities are inversely proportional if increase in one leads to decrease in the other

Examples
• Speed and time
• Number of workers and days

Mathematical Form
• x ∝ 1/y
• x × y = constant

RATIO AND FRACTION RELATION

• Ratio a:b can be written as fraction a/b
• Fraction can be converted into ratio

Example
• 3/5 = 3:5
• 2:7 = 2/7

RATIO AND PERCENTAGE LINK

Conversion
• Percentage = (Ratio value) × 100

Example
• Ratio 1:4 = 25 percent
• 2:5 = 40 percent

Used in
• Population growth
• Profit and loss
• Exam result analysis

DIVISION OF A QUANTITY IN A GIVEN RATIO

Formula
• Part = (Individual ratio term / Sum of ratio terms) × Total quantity

Example
• Divide 100 in ratio 2:3
• Parts = (2/5 × 100) and (3/5 × 100)

AGE-BASED RATIO QUESTIONS

Concept
• Age ratio remains constant over time
• Difference in age remains constant

Types
• Present age ratio
• Past age ratio
• Future age ratio

MIXTURE-BASED RATIO QUESTIONS

• Ratio used to compare components of mixture
• Used in milk-water, alcohol-water problems

PARTNERSHIP (INTRODUCTORY CONCEPT)

• Profit sharing is proportional to:
  Capital × Time

Basic Formula
• Profit ratio = (Capital × Time)

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Subject: CSAT

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